When the administrative agency not covered by the APA is a state agency rather than a local government or local administrative agency.
So held the 5th DCA in this opinion, in which it had to tussle through the various constitutional and rule provisions governing the review of administrative actions to come to a conclusion. I think they reached the right conclusion, but the fact that there's not statutory guidance on this issue is simply ridiculous.
The real conclusion: the Legislature should do its duty to proscribe by statute the authority of the different courts to hear APPEALs from administrative decisions. Basically we need a backup to Chapter 120 to cover all of those situations not covered by it - like local governments and boards, and state agencies that manage to get exemptions from the APA.